Treffer: A Mini-Max Variational Formula Giving Necessary and Sufficient Conditions for Recurrence or Transience of Multidimensional Diffusion Processes
Title:
A Mini-Max Variational Formula Giving Necessary and Sufficient Conditions for Recurrence or Transience of Multidimensional Diffusion Processes
Authors:
Publisher Information:
The Institute of Mathematical Statistics
Publication Year:
1988
Collection:
Project Euclid (Cornell University Library)
Subject Terms:
Document Type:
Fachzeitschrift
text
File Description:
application/pdf
Language:
English
ISBN:
978-1-176-99177-4
1-176-99177-9
1-176-99177-9
ISSN:
0091-1798
Relation:
http://projecteuclid.org/euclid.aop/1176991779; Ann. Probab. 16, no. 2 (1988), 662-671
DOI:
10.1214/aop/1176991779
Rights:
Copyright 1988 Institute of Mathematical Statistics
Accession Number:
edsbas.53B9EC36
Database:
BASE
Weitere Informationen
Let $L = \frac{1}{2} \nabla \cdot a\nabla + b \cdot \nabla$ generate a diffusion process on $R^d$. An expression involving $a$ and $b$ on $1 \leq |x| \leq n$ and two functions $g$ and $h$, varied over suitable domains, attains its mini-max value at $\lambda_n$. It is shown that $\lim_{n\rightarrow\infty}\lambda_n = 0$ or $\lim_{n\rightarrow\infty} \lambda_n > 0$ according to whether the process is recurrent or transient.